New fitting analyses for peak shapes in a 2D reciprocal-space map are demonstrated to evaluate the strain, strain distribution and domain size of a crystalline ultra-thin (15 Å ) film of -FeSi 2 (100) grown epitaxially on an Si(001) substrate, using grazing-incidence X-ray diffraction. A 2D Laue-fit analysis taking into account instrument broadening and the double-domain effect provides residual maps as a function of the inequivalent strains " b and " c along the b and c axes of -FeSi 2 , respectively (and domain size D), reflecting the probability of existence of homogeneous domains with fixed " b , " c and D, in addition to the most probable minimum residual. A 2D Laue fit with an inhomogeneous domain distribution provides a population map with " b and " c , reflecting strain components contributing to the film. The population map also leads to a reference residual as a guide for the strains contributing to the residual map. The advantages of the 2D Laue fits are discussed by comparison with the Scherrer, Williamson-Hall and Gaussian fitting methods for equivalent systems. The analyzed results indicate that the -FeSi 2 nanofilm was considerably small strained, which was also confirmed by transmission electron microscopy, implying a weak interface interaction between the film and the substrate.